Cement board

So I want to redo the bathroom in tile. All the way to the ceiling. Plus in the kitchen I want to throw stainless steel tile at the back wall by the stove, right up to the fume hood.

This raises questions.

First question of course is what do I do about the bathroom ceiling? The floor and walls will be cement board; the ceiling will be painted... painted drywall, or can/should I use cement board?

Second is should I use drywall/mastic in the kitchen, or cement board/thinset? If I go with cement board, should I do that just behind the stove, or also behind the sink, or go all the way and throw Hardiebacker against all the walls? If I put cement board behind the sink, how the heck do I paint it with all the not-smooth surface? Some kind of liberal use of latex-acrylic primer?

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